Question

If sec ø+tanø= P then show that p²-1/p²+1=sin ø
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Answer 1

Answer:

I hope ,this will help you

Step-by-step explanation:

Given that,

Secθ+tanθ=p..................(1)

⇒(Secθ+tanθ)(Secθ−tanθ)=1

⇒p(Secθ−tanθ)=1

⇒(Secθ−tanθ)=

p

1

.........(2)

Addequations(1)and(2)weget

⇒Secθ+tanθ+Secθ−tanθ=p+

p

1

⇒2secθ=

p

p

2

+1

⇒secθ=

2p

p

2

+1

∴cosθ=

p

2

+1

2p

sinθ=

1−cos

2

θ

=

1−(

p

2

+1

2p

)

2

=

(p

2

+1)

2

(p

2

+1)

2

−4p

2

=

(p

2

+1)

2

p

4

+2p

2

+1−4p

2

=

(p

2

+1)

2

p

4

−2p

2

+1

=

(p

2

+1)

2

(p

2

−1)

2

Hence,sinθ=

p

2

+1

p

2

−1